Question

Twenty students randomly assigned to an experimental group receive an instructional program; 30 in a control group do not. After 6 months, both groups are tested on their knowledge. The experimental group has a mean of 38 on the test (with an estimated population standard deviation of 3); the control group has a mean of 35 (with an estimated population standard deviation of 5). Using the .05 level, evaluate the researcher's hypothesis that the instructional program affects students' knowledge. What is the correct cutoff score(s)

Answer 1

The solution according to the problem given is provided below in the explanation segment.

Explanation:

According to the question,

`H_o: \mu_1=\mu_2`

`H_a: \mu_1 \\eq \mu_2`

Level of significance,

`\alpha = .05`

The test statistics will be:

⇒
`Z = \frac{(\bar x_1 - \bar x_2)}{\sqrt{(\sigma_1^2)/(n_1) +(\sigma_2^2)/(n_2) } }`

`=\frac{(38-35)}{\sqrt{((3)^2)/(30) +((5)^2)/(30) } }`

`=2.82`

The p-value will be:

=
`0.0024`